EduSahara™ Worksheet

Question 1

1.

The angles of depression of two boats from the top of a cliff 120 m high are 30° and 60° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .

(i)

134.56 m
(ii)

155.56 m
(iii)

114.56 m
(iv)

138.56 m

Question 2

2.

A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 60° and the angle of elevation of the top of the building is 30°. If the height of the building is 17 m, find the height of the flag staff .

(i)

29.00 m
(ii)

39.00 m
(iii)

31.00 m
(iv)

37.00 m
(v)

34.00 m

Question 3

3.

A
building
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
building
is found to be
30°
.
If the distance between the point and the foot of the
building
is
70 m
,
find the distance between
the observation point and the top of the
building
.

(i)

140

m
(ii)

140
3

√

3

m
(iii)

140
3

√

18

m
(iv)

140
3

m
(v)

70

√

2

m

Question 4

4.

A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 60° and the angle of elevation of the top of the building is 45°. If the height of the flag staff is 16 m, find the height of the building .

(i)

24.85 m
(ii)

18.85 m
(iii)

16.85 m
(iv)

26.85 m
(v)

21.85 m

Question 5

5.

From a point 90 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 60° and 45° respectively. Find the height of the pillar.

(i)

62.89 m
(ii)

60.89 m
(iii)

65.89 m
(iv)

68.89 m
(v)

70.89 m

Question 6

6.

A
building
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
building
is found to be
45°
.
If the distance between the point and the top of the
building
is
10 m
,
find the distance between
the observation point and the foot of the
building
.

(i)

10

√

3

m
(ii)

5
2

√

12

m
(iii)

5

m
(iv)

5

√

2

m
(v)

10

m

Question 7

7.

A
building
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
building
is found to be
60°
.
If the height of the
building
is
40 m
,
find the distance between
the observation point and the foot of the
building
.

(i)

40

m
(ii)

40
3

√

18

m
(iii)

20

√

2

m
(iv)

40
3

m
(v)

40
3

√

3

m

Question 8

8.

A boy standing on a vertical cliff in a jungle observes two rest houses in line with him on opposite sides deep in the jungle below. If their angles of depression are 45° and 30° and the distance between them is 200 m , find the height of the cliff.

(i)

68.21 m
(ii)

78.21 m
(iii)

70.21 m
(iv)

73.21 m
(v)

76.21 m

Question 9

9.

A
tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
tower
is found to be
45°
.
If the distance between the point and the foot of the
tower
is
180 m
,
find the height of the
tower
.

(i)

181

m
(ii)

183

m
(iii)

180

m
(iv)

177

m
(v)

179

m

Question 10

10.

A flagstaff stands on the top of a building at a distance of 20 m away from the foot of building . The angle of elevation of the top of the flagstaff is 45° and the angle of elevation of the top of the building is 30°. Find the height of the flagstaff .

(i)

(

20

−

20
3

√

3

)

m
(ii)

(

20

√

6

−

20
3

√

18

)

m
(iii)

(

2

−

√

3

)

m
(iv)

(

10

√

6

−

10

√

2

)

m
(v)

800
3

m

Question 11

11.

From a point 60 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 60° and 45° respectively. Find the height of the cliff.

(i)

55.00 m
(ii)

57.00 m
(iii)

60.00 m
(iv)

63.00 m
(v)

65.00 m

Question 12

12.

A
tower
stands vertically on the ground.

The height of the
tower
is
200

√

3

m
.

The distance between the observation point and its foot
is
600

m
.

Find the angle of elevation.

(i)

75°
(ii)

60°
(iii)

90°
(iv)

45°
(v)

30°

Question 13

13.

A man in a boat rowing away from a lighthouse 80 m high, takes 2 min to change the angle of elevation of the top of the lighthouse from 60° to 45°. Find the speed of the boat.

(i)

7.28 m/sec
(ii)

1.28 m/sec
(iii)

2.28 m/sec
(iv)

8.28 m/sec
(v)

0.28 m/sec

Question 14

14.

A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards him. If it takes 14 min for the angle of depression to change from 30° to 45°, how soon after this, will the car reach the observation tower?

(i)

22 min 15 sec
(ii)

19 min 8 sec
(iii)

16 min 10 sec
(iv)

18 min 12 sec
(v)

20 min 14 sec

Question 15

15.

A
chimney
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
chimney
is found to be
45°
.
If the height of the
chimney
is
140 m
,
find the distance between
the observation point and the top of the
chimney
.

(i)

140

√

2

m
(ii)

70

√

12

m
(iii)

280

m
(iv)

280

√

3

m
(v)

140

m

Question 16

16.

A
building
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
building
is found to be
30°
.
If the distance between the point and the top of the
building
is
50 m
,
find the height of the
building
.

(i)

23

m
(ii)

26

m
(iii)

27

m
(iv)

24

m
(v)

25

m

Question 17

17.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 20 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 45° respectively. Find the width of the river .

(i)

17.00 m
(ii)

25.00 m
(iii)

15.00 m
(iv)

20.00 m
(v)

23.00 m

Question 18

18.

Two vertical poles are on either side of a road. A 34 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 30° with the pole and when it is turned to rest against another pole, it makes an angle of 45° with the road. Find the width of the road.

(i)

56.49 m
(ii)

53.49 m
(iii)

48.49 m
(iv)

50.49 m
(v)

58.49 m

Question 19

19.

The shadow of a vertical tower BA on a level ground is increased by 20 m, when the altitude of the sun changes from 60° to 45°. Find the height of the tower .

(i)

50.32 m
(ii)

44.32 m
(iii)

47.32 m
(iv)

52.32 m
(v)

42.32 m

Question 20

20.

From the top of a 9 m high building , the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Find the height of the cable tower.

(i)

24.59 m
(ii)

21.59 m
(iii)

19.59 m
(iv)

27.59 m
(v)

29.59 m

Question 21

21.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 10 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 45° and 60° respectively. Find the height of the other temple.

(i)

5.23 m
(ii)

4.23 m
(iii)

6.23 m
(iv)

2.23 m
(v)

3.23 m

Question 22

22.

A man 1.9 m tall stands at a distance of 5.9 m from a lamp post and casts a shadow of 7.4 m on the ground. Find the height of the lamp post .

(i)

4.41 m
(ii)

5.41 m
(iii)

3.41 m
(iv)

2.41 m
(v)

1.41 m

Question 23

23.

An observer 1.8 m tall, is 170 m away from a tower . The angle of elevation of the top of the tower from her eyes is 45°. Find the height of the tower .

(i)

183.80 m
(ii)

157.80 m
(iii)

171.80 m
(iv)

186.80 m
(v)

154.80 m

Question 24

24.

The upper part of a tree is broken into two parts without being detatched. It makes an angle of 30° with the ground. The top of the tree touches the ground at a distance of 100 m from the foot of the tree . Find the height of the tree before it was broken.

(i)

146.21 m
(ii)

173.21 m
(iii)

186.21 m
(iv)

188.21 m
(v)

161.21 m

Question 25

25.

Two boys are on opposite sides of a tower of 170 m height. They measure the angle of elevation of the top of the tower as 60° and 30° respectively. Find the distance between the two boys.

(i)

340

√

2

m
(ii)

680

m
(iii)

680
3

√

18

m
(iv)

680
3

m
(v)

680
3

√

3

m

Assignment Key